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Chapter 7 Review
You Should Remember….
• A polynomial is an algebraic
expression consisting of one or more
terms separated by addition (+) or
subtraction (-) signs.
• 3x
3x+2
3x+2y+2
Is a monomial
Is a binomial
(it has ONE term)
(it has TWO terms)
Is a trinomial
(it has THREE terms)
Combining Like Terms
• Polynomials that are the SAME can be combined.
In order for a polynomial to be considered the
SAME they must have the same LITERAL
coefficient.
• The non-numeric (letter) of a term is it’s literal
coefficient.
• For example: 2x and 3x are like terms because
they both have an x as their literal coefficient.
Therefore they can be combined.
• Ex. 2x + 3x = 5x
Like terms….
• You can also think of terms as tiles;
if they are the same tile, they are
like terms and they can be combined.
• Ex:
x + x = 2x
Common Factors
• Factors are the numbers that are multiplied to
produce a specific product.
• For example the factors of 12 are:
1 and 12; 2 and 6; 3 and 4
• Common factors are the factors that 2 or more
terms have in common.
• For example: 12 and 6 both have 1, 2, 3, 6 as
factors. Their GCF (greatest common factor is 6.
Common Factors of
Polynomials
• There are 2 ways to find the common
factors of a polynomial:
– the sharing model (which works well
when the common factor is a numerical)
– the area model (which works well when
the common factor is literal)
Sharing Model
• The sharing model is used to put a
polynomial in a number of groups with
each group having the same tiles.
• For example: 3x + 12 can be made into
3 groups with x + 4 in each group.
Area Model
• In the area model, the tiles are
arranged to form a rectangle and
then the dimension of the rectangle
are found: width = 3 length = x + 4
3
X+4
Area Model…
• This rectangle has an area of x2 + 2x
and it’s dimensions are x and x + 2
X
x2
x
X+2
x
Chapter 7 Review
• Page. 362-363
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